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Francois Ziegler
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Original reference for Adams-Riemann Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote by $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(T_f)$ the $j$-th canibalisticcannibalistic class of the relative tangent bundle $T_f$. The Adams-Riemann Riemann-Roch theorem states that for any $j$ the diagram $$ \begin{matrix} \phantom{aaaa}K_0(Y) & \xrightarrow{f_*} & K_0(X)\\ ^{\theta^j(T_f)\cdot \psi^j}\downarrow & & \downarrow ^{\psi^j}\\ K_0(Y)\otimes\mathbb{Z}[\frac{1}{j}] & \xrightarrow{f_*} & K_0(X) \otimes \mathbb{Z}[\frac{1}{j}] \end{matrix} $$$\require{AMScd}$ $$ \begin{CD} K_0(Y)@>f_*>>K_0(X)\\ @V\theta^j(T_f)\cdot \psi^jVV@VV\psi^jV\\ K_0(Y)\otimes\mathbb{Z}[\tfrac{1}{j}]@>f_*>>K_0(X) \otimes \mathbb{Z}[\tfrac{1}{j}] \end{CD} $$ commutes.

The oldest reference I know is Theorem 7.6 of Chapter V in W. Fulton; S. Lang: Riemann-Roch algebra. Grundlehren der Mathematischen Wissenschaften , 277. Springer-Verlag, New York, 1985. x+203 pp.. However, that reference is already very general (it does not even require schemes to be over a field) and 1985 is very "late" for such a Riemann-Roch type statement. Therefore my question:

$ \phantom{aaaaaaaa}$What is the original reference for the Adams-Riemann Riemann-Roch theorem?

I am looking for something as Borel-Serre's paper is for Grothendieck-Riemann-Roch.

Original reference for Adams-Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(T_f)$ the $j$-th canibalistic class of the relative tangent bundle $T_f$. The Adams-Riemann-Roch states that for any $j$ the diagram $$ \begin{matrix} \phantom{aaaa}K_0(Y) & \xrightarrow{f_*} & K_0(X)\\ ^{\theta^j(T_f)\cdot \psi^j}\downarrow & & \downarrow ^{\psi^j}\\ K_0(Y)\otimes\mathbb{Z}[\frac{1}{j}] & \xrightarrow{f_*} & K_0(X) \otimes \mathbb{Z}[\frac{1}{j}] \end{matrix} $$ commutes.

The oldest reference I know is Theorem 7.6 of Chapter V in W. Fulton; S. Lang: Riemann-Roch algebra. Grundlehren der Mathematischen Wissenschaften , 277. Springer-Verlag, New York, 1985. x+203 pp.. However, that reference is already very general (it does not even require schemes to be over a field) and 1985 is very "late" for such a Riemann-Roch type statement. Therefore my question:

$ \phantom{aaaaaaaa}$What is the original reference for the Adams-Riemann-Roch theorem?

I am looking for something as Borel-Serre's paper is for Grothendieck-Riemann-Roch.

Original reference for Adams Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote by $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(T_f)$ the $j$-th cannibalistic class of the relative tangent bundle $T_f$. The Adams Riemann-Roch theorem states that for any $j$ the diagram $\require{AMScd}$ $$ \begin{CD} K_0(Y)@>f_*>>K_0(X)\\ @V\theta^j(T_f)\cdot \psi^jVV@VV\psi^jV\\ K_0(Y)\otimes\mathbb{Z}[\tfrac{1}{j}]@>f_*>>K_0(X) \otimes \mathbb{Z}[\tfrac{1}{j}] \end{CD} $$ commutes.

The oldest reference I know is Theorem 7.6 of Chapter V in W. Fulton; S. Lang: Riemann-Roch algebra. Grundlehren der Mathematischen Wissenschaften , 277. Springer-Verlag, New York, 1985. x+203 pp.. However, that reference is already very general (it does not even require schemes to be over a field) and 1985 is very "late" for such a Riemann-Roch type statement. Therefore my question:

$ \phantom{aaaaaaaa}$What is the original reference for the Adams Riemann-Roch theorem?

I am looking for something as Borel-Serre's paper is for Grothendieck-Riemann-Roch.

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Tintin
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Original reference for Adams-Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(T_f)$ the $j$-th canibalistic class of the relative tangent bundle $T_f$. The Adams-Riemann-Roch states that for any $j$ the diagram $$ \begin{matrix} \phantom{aaaa}K_0(Y) & \xrightarrow{f_*} & K_0(X)\\ ^{\theta^j(T_f)\cdot \psi^j}\downarrow & & \downarrow ^{\psi^j}\\ K_0(Y)\otimes\mathbb{Z}[\frac{1}{j}] & \xrightarrow{f_*} & K_0(X) \otimes \mathbb{Z}[\frac{1}{j}] \end{matrix} $$ commutes.

The oldest reference I know is Theorem 7.6 of Chapter V in W. Fulton; S. Lang: Riemann-Roch algebra. Grundlehren der Mathematischen Wissenschaften , 277. Springer-Verlag, New York, 1985. x+203 pp.. However, that reference is already very general (it does not even require schemes to be over a field) and 1985 is very "late" for such a Riemann-Roch type statement. Therefore my question:

$ \phantom{aaaaaaaa}$What is the original reference for the Adams-Riemann-Roch theorem?

I am looking for something as Borel-Serre's paper is for Grothendieck-Riemann-Roch.